Circle Problem!

Geometry Level pending

Assume you have an empty plane.In that plane there is a straight line.Tangent to the line ,above it,we have $3$ circles which are also tangent to each other.There is one small circle in the middle.In the left there is a big circle and in the right there is an average circle.If the radius of the big circle and average circle are $72$ and $18$ respectively,then find the radius of the smaller circle.(Yes, the big circle and the average circle are tangent to each other and to the small circle in the middle simultaneously.)

The answer is 8.

1 solution

Patrick Corn
Sep 3, 2014

In general for radii $a$ and $b$ , the solution is $\frac{ab}{(\sqrt{a}+\sqrt{b})^2}$ . Plugging in $72$ and $18$ gives $\fbox{8}$ .

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Circle Problem!

The answer is 8.

1 solution

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